Already known is a method for cooling hot wire in air. The wire, coiled vertically and in spaced windings, is inserted into a duct or shaft. The coils are transported down the duct by means of a number of endless conveyor chains equipped with spaced fingers protruding toward the duct interior in a star-like arrangement. The coiled wire windings are deposited sequentially on the fingers. The finished bundle is removed at the lower end of the duct. Furthermore, it is known to treat steel wire by cooling in a lead bath or in a saline smelt. In this method, the wire is pulled through a tub containing the liquid medium. The disadvantage of such an installation is the space requirements, particularly if the installation has a large capacity, and the wire passes through at a correspondingly high speed, as the treatment line must be of suitable length to provide the required retention period for exposure to treatment.